Here is a problem in which I need to have employees scheduled for shifts that be

Question

Here is a problem in which I need to have employees scheduled for shifts that begin at 8:00 a.m.; Noon; 4:00 p.m.; 8:00 p.m. and Midnight. The minimum number of officers must be at least what is listed in column C. I know that a+b+c+d+e+f >=0. I don't know how to finish writing the objective function or to calculate the constraints. Please provide in detail the formulas so I can complete this problem. Time of Day Min Officers 8 a.m.-4 p.m. Noon-8 p.m. 4 p.m.-midnight a+b+c+d+e+f+g 8 p.m.-4 a.m. Midnight-8 a.m. RHS a 8 a.m. - Noon 5 a+b>=5 b Noon-4:00 p.m. 6 b+c>=6 c 4 p.m.-8 p.m. 10 c+d>=10 d 8 p.m.-Midnight 7 d+e>=7 e Midnight-4 a.m. 4 e+f>=4 f 4 a.m.-8 a.m. 6 f+g>=6 Here is a problem in which I need to have employees scheduled for shifts that begin at 8:00 a.m.; Noon; 4:00 p.m.; 8:00 p.m. and Midnight. The minimum number of officers must be at least what is listed in column C. I know that a+b+c+d+e+f >=0. I don't know how to finish writing the objective function or to calculate the constraints. Please provide in detail the formulas so I can complete this problem. Time of Day Min Officers 8 a.m.-4 p.m. Noon-8 p.m. 4 p.m.-midnight a+b+c+d+e+f+g 8 p.m.-4 a.m. Midnight-8 a.m. RHS a 8 a.m. - Noon 5 a+b>=5 b Noon-4:00 p.m. 6 b+c>=6 c 4 p.m.-8 p.m. 10 c+d>=10 d 8 p.m.-Midnight 7 d+e>=7 e Midnight-4 a.m. 4 e+f>=4 f 4 a.m.-8 a.m. 6 f+g>=6

Explanation / Answer

The objective function is to minimize the total number of employees.

Thus, minimize : a+b+c . . . + f subject to constraints:

a >= 5 ; b >=6; c >=10, d >=7 ; e >= 4; f >=6

and, a+b >=6; b+c>=10; c+d >=10;d+e >=7, e+f>=6

The last set of constraints are from the fact that, minimum requirement for a shift from 8 am to 4p.m would be the bigger of the minimum requirements of 8a.m. - Noon and Noon-4p.m. and so on.

Hope, now you can solve this. Ask if you have any doubts.

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